This activity involves rounding four-digit numbers to the nearest thousand.

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

This challenge asks you to imagine a snake coiling on itself.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Can you explain the strategy for winning this game with any target?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Here are two kinds of spirals for you to explore. What do you notice?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Delight your friends with this cunning trick! Can you explain how it works?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

This task follows on from Build it Up and takes the ideas into three dimensions!

Got It game for an adult and child. How can you play so that you know you will always win?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Are these statements always true, sometimes true or never true?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Find out what a "fault-free" rectangle is and try to make some of your own.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

How many centimetres of rope will I need to make another mat just like the one I have here?

An investigation that gives you the opportunity to make and justify predictions.

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?